For supercritical multitype branching processes in continuous time, weinvestigate the evolution of types along those lineages that survive up to sometime t. We establish almost-sure convergence theorems for both time andpopulation averages of ancestral types (conditioned on non-extinction), andidentify the mutation process describing the type evolution along typicallineages. An important tool is a representation of the family tree in terms ofa suitable size-biased tree with trunk. As a by-product, this representationallows a `conceptual proof' (in the sense of Kurtz, Lyons, Pemantle, Peres1997) of the continuous-time version of the Kesten-Stigum theorem.